MOSCOW, April 2 (Reuters) - Russian President Vladimir Putin has formally divorced his wife Lyudmila after more than 30 years of marriage, Kremlin spokesman said on Wednesday, following a surprise breakup announcement last year.

"The divorce has taken place," Dmitry Peskov said, without giving any further details.

Putin and his wife announced that their marriage was over last June in a live broadcast on Russian state television, confirming longstanding speculation that they had separated.

The Kremlin made clear at the time that their breakup had yet to be formalised.

The ex-KGB spy, 61, keeps his personal life private and little is known about his wife and two daughters, both in their 20s.

In 2008, Putin said there was no truth to a newspaper report that he was preparing to marry Olympic rhythmic gymnast Alina Kabayeva, who was born in 1983, the same year he married Lyudmila.

Putin told journalists to keep their "snotty noses" out of his private affairs and the newspaper, Moskovsky Korrespondent, folded shortly afterwards.

Kabayeva, who was one of the torch bearers at the Sochi Olympics opening ceremony in February, also denied any relationship with Putin. (Reporting by Alexei Anishchuk; Editing by Sonya Hepinstall)